This study aims to develop a two-stage Bayesian optimization framework to improve multiphysics electric-machine design, targeting high performance under stringent electromagnetic, thermal, mechanical and economic constraints while keeping finite-element evaluation costs manageable.
Stage I performs a multi-objective tree-structured Parzen estimator (TPE) search to map efficiency–power–cost trade-offs and build a Pareto surrogate. Stage II applies permutation-importance screening and an improved, constraint-aware TPE with dynamic sample filtering to refine key parameters near the feasible boundary.
In a surface-mounted permanent-magnet synchronous motor case, the proposed method produced 48 designs meeting six hard constraints, including = 93% system efficiency and slot fill = 0.85, within 1,147 finite-element runs. It yielded over an order of magnitude more feasible, high-performance designs than single-stage or unrefined two-stage baselines at identical computational budgets.
The framework is the first, to the best of the authors’ knowledge, to integrate explainable permutation importance with dynamically reweighted TPE sampling for constrained electric-machine optimization, simultaneously enhancing feasibility, performance and parameter diversity. It offers a transferable, lightweight template that augments existing multiphysics workflows without altering underlying solvers, supporting better engineering and manufacturing decisions.
